The msf file is of no use to you; it's a summary or index file, and does not itself hold the message text. You want the accompanying extension-less mailbox file. *.msf files can be deleted and will be rebuilt automatically as and when needed.

My expectation is that if you simply copy the mailbox file into your new profile it should just magically appear, but the only safe place to put it is under Local Folders. Once there, you can move or copy its contents to somewhere else as suits your needs. Or you could use the https://nic-nac-project.org/~kaosmos/mboximport-en.html to import selected folders or mailboxes from an old profile.

If the volume of material isn't too great, simply setting up an IMAP-connected account on both machines may be the easiest way to get emails messages from one to the other. ;-)

I have moved complete Thunderbird profiles from Windows to Linux myself, and didn't encounter any of the line-ending issues that I expected and indeed that other users report. My only woes were the different conventions used in pathnames, particularly within extensions and add-ons who use absolute rather than relative pathnames.

Here is the problem I have. If I copy the inbox files then I will lose all the current messages on my Linux box. I want to ADD the messages from my windows machine to my Linux Thunderbird. Will the import utility do this? And if so how do I export from windows TB?

They are files. You can rename them to give them unique names, and copy them into Local Folders on the target machine.

Or use IMAP and do it via the email server.